Trigonometric approximation of functions in \(L _{p}\)-norm
This is a very nice paper. The author investigates trigonometric polynomials associated with \(f\in \text{Lip}(\alpha, p)\) (\(0<\alpha\leq 1\), \(p\geq 1\)) to approximate \(f\) in \(L_p\)-norm to the degree of \(O(n^{-\alpha})\) \((0<\alpha\leq 1)\). The most interesting results treat the case \(\alpha= 1\). His three new theorems have numerous attractive corollaries, some of them give sharper estimates than the known ones.
scientific article; zbMATH DE number 1866667
scientific article